Since the DarkSide-50 experiment has not detected any WIMP event,
limits for each of the 12 cross sections \(\sigma _i\)  are given as a function of the
WIMP mass \(M_\chi \) . Figure REF  shows the normalized shape of the recoil energy
for five selected operators in an argon detector with the acceptance of
DarkSide-50 [1]}. The solid curve (number 3) corresponds
to the standard SI operator.
The other four curves are examples which give the most extreme results in terms of the final WIMP-nucleus cross-section exclusion limits for each of the two response functions \(\Phi ^{\prime \prime }\)  and \(M\) .
Given enough WIMP events the recoil spectrum should make it possible to distinguish between different interaction models. A statistical analysis that takes into account the different expected recoil spectra gives stronger exclusion curves if background is present; this is not our case, since the DarkSide-50 experiment has a total expected background after the selection of only about 0.1 events.
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